WASHINGTON (Reuters) - Vatican-convened talks between Venezuela's government and opposition are the last, best chance to find a peaceful solution to the country's political impasse, U.S. Undersecretary of State for Political Affairs Tom Shannon said on Friday.

In his first remarks since visiting Caracas on Monday, Shannon said Washington would support the talks "as long as it remains viable."

"From our point of view (the dialogue) really is the last best effort to try to find a negotiated, peaceful solution to this," he told reporters. "Absent this dialogue process, Venezuela will find itself in a state in which both the government and the opposition will have to measure themselves through their ability to put people on to the streets."

He said that this kind of mobilization would be "unpredictable and can be very dangerous."

Shannon traveled to Caracas on Oct. 31, a day after initial talks led by the Vatican. He has spearheaded efforts by the Obama administration to ease tensions with Venezuela, which often accuses Washington of trying to topple President Nicolas Maduro's government.

Maduro's adversaries accuse him of creating a dictatorship by blocking a recall referendum on his rule and of illegally overriding the legislature, which was taken over by the opposition in a landslide election last year.

The opposition insists the government allow the referendum, release dozens of jailed opposition activists and respect congressional decisions.

There is no indication Maduro will agree to any of the opposition's demands, and in a speech on Thursday he criticized their timetable and urged patience.

"It is a fragile but very important process, and it's a good faith effort to find a peaceful way out of the political impasse that has crippled Venezuela," said Shannon, who described the negotiations as "the only game in town."

The Vatican, which was instrumental in restoring relations between the United States and Cuba last year, faces a difficult situation in Venezuela, given the few signs of agreement between Maduro and the opposition.

Shannon described the initial meeting as "a huge step" but said the opposition wanted more gestures from the government ahead of the next round of talks on Nov. 11. This included a significant release of political prisoners, he added.

"How the issue of prisoners is dealt with is obviously going to be key to the success of this process going forward," he said, adding that the sides would try to agree on an electoral agenda.